The present invention relates to an inference device which determines an estimated quantity such as control quantity from input data or which conducts a membership estimation in pattern recognition.
In a control system a final inference operational quantity may be determined using indefinite variables judged sensuously by an operator, for example, "big", "medium", etc. An inference device based on fuzzy inference employs fuzzy variables as indefinite variables in an inference rule of the "IF--THEN--" type.
FIG. 5 shows one exampiLe of fuzzy variables. In FIG. 5, NB denotes Negative Big, NM denotes Negative Medium, NS denotes Negative Small, ZO denotes Zero, PS denotes Positive Small, PM denotes Positive Medium and PB denotes Positive Big. In fuzzy inference, a fuzzy variable is always written in an antecedent (IF part) of the inference rule, while a fuzzy variable or an equation is written in a consequent (THEN part) of the inference rule. When a real number or a fuzzy number is inputted, as data, to the inference device in the case where the fuzzy variable is written in the consequent, the inference device calculates the degree of matching (membership value) between the real number or the fuzzy number and a membership function indicative of the fuzzy variable of the antecedent and determines an output fuzzy number of the consequent through a plurality of processings of the degree of matching. It is possible to obtain an actual operational quantity by taking a value of center of gravity, etc. of output fuzzy numbers based on a plurality of rules. Meanwhile, in the case where the equation is written in the consequent, the actual operational quantity can be obtained without performing the processing of taking the value of center of gravity, etc.
One of the conventional inference methods using this fuzzy inference is fuzzy modelling disclosed, for example, by Geun-Taek Kang and Michio Sngeno in a paper entitled "Fuzzy modelling" of SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS PAPERS, Vol. 23, No. 6, pp. 650-652, 1987.
On the other hand, a method of and a device for automatically determining the membership function indicative of the fuzzy number and shape of the inference rule by introducing the learning property of a neural network into fuzzy modelling are proposed in U.S. patent application Ser. No. 459,815 by two inventors including one of the present inventors. This method is a kind of fuzzy modelling, but is different from fuzzy modelling in that the learning property of the neural network is introduced thereinto. The neural network is a mathematical network which simulates connection of cranial nerve cells. In the neural network, a nonlinear problem can be solved by sequentially determining the strength of connection among units constituting the neural network.
FIG. 12 shows one example of known fuzzy inference devices. The known fuzzy inference device includes inference rule executors 1201 to 120r provided for inference rules, respectively, and an inference operational quantity determiner 1203 for determining a final inference operational quantity from estimated values obtained for the inference rules, respectively. Each of the inference rule executors 1201 to 120r is constituted by two portions. Namely, the inference rule executors 1201 to 120r include membership value estimators 1211 to 121r for identifying antecedents of the inference rules and inference operational quantity estimators 1221 to 122r for identifying consequents of the inference rules.
As shown in FIG. 9, the membership value estimators 1211 to 121r and the inference operational quantity estimators 1221 to 122r have the structure of a multilayered network. In FIG. 9, reference numeral 91 denotes a multi-input/multi-output signal processor and reference numeral 92 denotes an input terminal of the neural network model. For each of the inference rules, each of the membership value estimators 1211 to 121r and each of the inference operational quantity estimators 1221 to 122r shown in FIG. 12 identify structures of the antecedent and the consequent, respectively, and obtains from a given input value, a variable of a formula indicative of an estimated value of the membership value of the antecedent and an inference operational quantity of the consequent. In accordance with each inference rule thus obtained, the inference operational quantity determiner 1203 determines the final inference operational quantity.
One example of the operation of the known fuzzy inference device of FIG. 12 is described by using numerals indicated by Tadashi Kondo in a paper entitled "Revised GMDH Algorithm Estimating Degree of the Complete Polynomial" of SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS PAPERS, Vol. 22, No. 9, pp. 928-934, 1986. The calculation algorithm is as follows.